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www.logicmatters.net | ||
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www.umsu.de
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| | | | | [AI summary] The discussion centers on the interpretation of higher-order logic and the role of metaphysical domains. Andrew Bacon argues that higher-order logic doesn't require a metaphysical commitment to domains of objects, properties, or propositions. Instead, he emphasizes the use of stipulative definitions and logical connections between sentences to interpret expressions. He contrasts this with the idea that models must be interpreted in a way that reflects a metaphysical structure of reality. The conversation also touches on the nature of provability operators and their relationship to logical frameworks, highlighting the distinction between formal languages and their interpretations in different contexts. | |
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xorshammer.com
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| | | | | Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that... | |
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lawrencecpaulson.github.io
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ischoolonline.berkeley.edu
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| | | Whether you know it or not, you've probably been taking advantage of the benefits of machine learning for years. Most of us would find it hard to go a full day without using at least one app or web service driven by machine learning. But what is machine learning? | ||
